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According to census data in 1950 the population of the US amounted to 151.3 million persons.

This question aims to find the practical and statistical significance of the difference in percentages of two different populations. In the 1950s, the population of the US amounted to 151.3 million persons and 13.4 % of them were living in the West according to census data. This population percentage increased to 281.4 million and 22.5 % of them were living in the West in the year 2000.

If we gather the percentage of the population living in the West then we come to know that, only 13.4% of the total population of the US was living in the West in the 1950s while this percentage increased to 22.5% of the total population in 2000.

We can find significance by applying two sample z-test. It is the hypothetical testing of the statistical data of two samples to determine that the mean of the difference between two populations is not statistically significant. Knowing the standard deviation of two populations is an important tool for applying this test.

Expert Answer

If we take the difference between both percentages, we can easily tell the increase in population over 50 years.

\[Difference = 22.5 – 13.4\] 

\[Difference = 9.1\]

9.1% is a large difference in percentages, which means the difference in percentages is partially significant.

To check whether the difference is statistically significant, two sample z-test is conducted. This test is only useful to check significance when the given samples are simple random samples.

If every sample from the samples of size n has an equal probability of being chosen, then this is called random sampling. It is the best way of making inferences about statistical data. It helps to make an unbiased choice among the large population.

According to the given data, each individual among the population is representing a sample which means samples are not simple random samples. Therefore, it is not appropriate to find the statistical significance of the difference.

Numerical Results

The samples are not probability samples, so it is not possible to determine whether the difference in percentages is statistically significant or not.

The statistical significance of the difference in population percentages cannot be determined.

Example

The population of Asia increased from 3.1 billion in the 1990s to 4.7 billion in 2018. 17% of the population of Asia was living in the South in the 1990s while 25% population started to live in the South side in 2018. Find the statistical significance of the difference in population.

To find the statistical significance of the difference in population by using two sample z-test.

If we take the difference between both percentages, we can easily tell the increase in population from the 1990s to 2018.

\[Difference=25 – 17\]

\[Difference = 8\]

The difference in population is 8%.

Since the individuals represent samples of the population that means the samples are not simple random samples.

The statistical significance of these samples cannot be determined.

Image/Mathematical drawings are created in Geogebra.

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